Decomposition matrices for spin characters of symmetric groups. (English) Zbl 0651.20007

Morris, A. O.; Yaseen, A. K.

Proc. R. Soc. Edinb., Sect. A 108, No. 1-2, 145-164 (1988).

Let \(\tilde S_ n\) be a double cover of the symmetric group \(S_ n\). The faithful irreducible characters of \(\tilde S_ n\) are called spin characters. In this paper a study of the p-decomposition numbers of such characters is initiated for odd prime integers p. A general technique is developed by a non-trivial modification of a corresponding technique for the characters of \(S_ n\). Then the decomposition numbers are determined explicitly for \(p=3\) and \(3\leq n\leq 11\) with an ambiguity for \(n=9\). The second author will deal separately with the cases \(p=5,7,11\).

Reviewer: J.B.Olsson

MSC:

20C30	Representations of finite symmetric groups
20C20	Modular representations and characters
20C25	Projective representations and multipliers

Keywords:

double cover; symmetric group; faithful irreducible characters; spin characters; decomposition numbers

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